duahsolo wrote:
Which of the following is closest to the difference between sum of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
A) 2.82
B) 2.72
C) 1.82
D) 1.72
E) 0.82
The question is a bit tricky because of the word digit. Most people assume it to be numbers and are do calculations for values of x upto infinity..
So, 1st term = 1/2 +1/3+1/4+1/5+1/6+1/7+1/8 +1/9
=(1/2+1/4+1/8)+(1/3+1/6+1/9)+(1/5+1/7)
=(0.500+0.250+0.125) +(0.333+0.167 +0.111)+(0.200+0.143)
= 0.875 +0.611+0.343
=1.829
2nd term = 1/2*2/3*....*8/9 = 1/9 = 0.111
So, 1st term - 2nd term = 1.829 - 0.111 = 1.718 ~ 1.72
Answer D
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